Abstract

We report the transmission anomaly in a modified slit grating, which is dressed, on the slit sidewalls, with the linear chains of metal bumps. An asymmetric lineshape, which is characteristic of the Fano resonance, has been found in a narrow frequency range of the spectrum. The effect can be attributed to the interference between nonresonant background transmission and resonant plasmonic wave excitation in the linear chains. The dispersion of chain plasmon mode has been suggested, enabling the dynamic tuning of spectral position of the Fano effect.

© 2011 OSA

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  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
    [CrossRef]
  2. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
    [CrossRef] [PubMed]
  3. H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
    [CrossRef] [PubMed]
  4. X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett. 105(24), 243901 (2010).
    [CrossRef]
  5. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
    [CrossRef]
  6. M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).
    [CrossRef]
  7. C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003).
    [CrossRef]
  8. W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
    [CrossRef] [PubMed]
  9. S. H. Chang, S. K. Gray, and G. C. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005).
    [CrossRef] [PubMed]
  10. T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
    [CrossRef] [PubMed]
  11. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
    [CrossRef]
  12. K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, “Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,” Phys. Rev. Lett. 88(25), 256806 (2002).
    [CrossRef] [PubMed]
  13. M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
    [CrossRef] [PubMed]
  14. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
    [CrossRef] [PubMed]
  15. X. G. Yin, C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Transmission resonance in a composite plasmonic structure,” Phys. Rev. B 79(15), 153404 (2009).
    [CrossRef]
  16. X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
    [CrossRef]
  17. K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
    [CrossRef] [PubMed]
  18. D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
    [CrossRef]
  19. Here, for simplicity, the potential contribution from the neighbor charges has been neglected. The counting of neighbor contribution will add more circuit parameters and modify (enlarge) the chain-mode dispersion. Nonetheless, no further physical understanding can be provided.
  20. C. P. Huang, X. G. Yin, H. Huang, and Y. Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express 17(8), 6407–6413 (2009).
    [CrossRef] [PubMed]
  21. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
    [CrossRef] [PubMed]
  22. C. P. Huang, X. G. Yin, L. B. Kong, and Y. Y. Zhu, “Interactions of nanorod particles in the strong coupling regime,” J. Phys. Chem. C 114(49), 21123–21131 (2010).
    [CrossRef]
  23. C. Kittel, Introduction to Solid State Physics (Wiley, 2005).
  24. H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
    [CrossRef]
  25. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
    [CrossRef] [PubMed]

2010 (4)

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett. 105(24), 243901 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

C. P. Huang, X. G. Yin, L. B. Kong, and Y. Y. Zhu, “Interactions of nanorod particles in the strong coupling regime,” J. Phys. Chem. C 114(49), 21123–21131 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

2009 (5)

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

C. P. Huang, X. G. Yin, H. Huang, and Y. Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express 17(8), 6407–6413 (2009).
[CrossRef] [PubMed]

X. G. Yin, C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Transmission resonance in a composite plasmonic structure,” Phys. Rev. B 79(15), 153404 (2009).
[CrossRef]

X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
[CrossRef]

2008 (2)

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[CrossRef] [PubMed]

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

2007 (1)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

2005 (5)

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
[CrossRef] [PubMed]

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

S. H. Chang, S. K. Gray, and G. C. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

2003 (2)

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).
[CrossRef]

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003).
[CrossRef]

2002 (1)

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, “Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,” Phys. Rev. Lett. 88(25), 256806 (2002).
[CrossRef] [PubMed]

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Aikawa, H.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, “Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,” Phys. Rev. Lett. 88(25), 256806 (2002).
[CrossRef] [PubMed]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Brueck, S. R. J.

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

Byun, Y. M.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Chang, S. H.

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Fan, R. H.

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett. 105(24), 243901 (2010).
[CrossRef]

Fan, W. J.

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Genet, C.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003).
[CrossRef]

Ghaemi, H. F.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Gray, S. K.

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Huang, C. P.

C. P. Huang, X. G. Yin, L. B. Kong, and Y. Y. Zhu, “Interactions of nanorod particles in the strong coupling regime,” J. Phys. Chem. C 114(49), 21123–21131 (2010).
[CrossRef]

C. P. Huang, X. G. Yin, H. Huang, and Y. Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express 17(8), 6407–6413 (2009).
[CrossRef] [PubMed]

X. G. Yin, C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Transmission resonance in a composite plasmonic structure,” Phys. Rev. B 79(15), 153404 (2009).
[CrossRef]

X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
[CrossRef]

Huang, H.

Huang, X. R.

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett. 105(24), 243901 (2010).
[CrossRef]

Inoue, M.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Iye, Y.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, “Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,” Phys. Rev. Lett. 88(25), 256806 (2002).
[CrossRef] [PubMed]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Kang, J. H.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

Katsumoto, S.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, “Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,” Phys. Rev. Lett. 88(25), 256806 (2002).
[CrossRef] [PubMed]

Khanikaev, A. B.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Kihm, H. W.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

Kim, D. S.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

Kobayashi, K.

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, “Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,” Phys. Rev. Lett. 88(25), 256806 (2002).
[CrossRef] [PubMed]

Kong, L. B.

C. P. Huang, X. G. Yin, L. B. Kong, and Y. Y. Zhu, “Interactions of nanorod particles in the strong coupling regime,” J. Phys. Chem. C 114(49), 21123–21131 (2010).
[CrossRef]

Koschny, T.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Lalanne, P.

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[CrossRef] [PubMed]

Lee, K. G.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
[CrossRef] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

Li, J. Q.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Li, T.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Lienau, C.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

Limonov, M. F.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Liu, H.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Liu, H. T.

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[CrossRef] [PubMed]

Liu, Z. W.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Malloy, K. J.

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

Matsui, T.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Minhas, B.

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

Nahata, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Park, D. J.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

Park, Q. H.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Peng, R. W.

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett. 105(24), 243901 (2010).
[CrossRef]

Ropers, C.

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

Rybin, M. V.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Samusev, K. B.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Sarrazin, M.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).
[CrossRef]

Schatz, G. C.

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Shen, Z. Q.

X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
[CrossRef]

Soukoulis, C. M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Steel, M. J.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Thio, T.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

van Exter, M. P.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003).
[CrossRef]

Vardeny, Z. V.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

Vigneron, J. P.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).
[CrossRef]

Vigoureux, J. M.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).
[CrossRef]

Wang, Q. J.

X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
[CrossRef]

X. G. Yin, C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Transmission resonance in a composite plasmonic structure,” Phys. Rev. B 79(15), 153404 (2009).
[CrossRef]

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Wang, S. M.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Wei, Q. H.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Woerdman, J. P.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Yin, X. G.

C. P. Huang, X. G. Yin, L. B. Kong, and Y. Y. Zhu, “Interactions of nanorod particles in the strong coupling regime,” J. Phys. Chem. C 114(49), 21123–21131 (2010).
[CrossRef]

C. P. Huang, X. G. Yin, H. Huang, and Y. Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express 17(8), 6407–6413 (2009).
[CrossRef] [PubMed]

X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
[CrossRef]

X. G. Yin, C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Transmission resonance in a composite plasmonic structure,” Phys. Rev. B 79(15), 153404 (2009).
[CrossRef]

Yushin, G.

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Zhang, S.

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

Zhang, X.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Zhu, S. N.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Zhu, Y. Y.

C. P. Huang, X. G. Yin, L. B. Kong, and Y. Y. Zhu, “Interactions of nanorod particles in the strong coupling regime,” J. Phys. Chem. C 114(49), 21123–21131 (2010).
[CrossRef]

C. P. Huang, X. G. Yin, H. Huang, and Y. Y. Zhu, “Study of plasmon resonance in a gold nanorod with an LC circuit model,” Opt. Express 17(8), 6407–6413 (2009).
[CrossRef] [PubMed]

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

X. G. Yin, C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Transmission resonance in a composite plasmonic structure,” Phys. Rev. B 79(15), 153404 (2009).
[CrossRef]

X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
[CrossRef]

Zhu, Z. H.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

X. G. Yin, C. P. Huang, Z. Q. Shen, Q. J. Wang, and Y. Y. Zhu, “Splitting of transmission peak due to the hole symmetry breaking,” Appl. Phys. Lett. 94(16), 161904 (2009).
[CrossRef]

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93(7), 073109 (2008).
[CrossRef]

J. Phys. Chem. C (1)

C. P. Huang, X. G. Yin, L. B. Kong, and Y. Y. Zhu, “Interactions of nanorod particles in the strong coupling regime,” J. Phys. Chem. C 114(49), 21123–21131 (2010).
[CrossRef]

Nano Lett. (1)

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

Nat. Mater. (2)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[CrossRef] [PubMed]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Nature (3)

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446(7135), 517–521 (2007).
[CrossRef] [PubMed]

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452(7188), 728–731 (2008).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Opt. Commun. (1)

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003).
[CrossRef]

Opt. Express (2)

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Phys. Rev. B (4)

X. G. Yin, C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Transmission resonance in a composite plasmonic structure,” Phys. Rev. B 79(15), 153404 (2009).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).
[CrossRef]

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009).
[CrossRef]

Phys. Rev. Lett. (6)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

X. R. Huang, R. W. Peng, and R. H. Fan, “Making metals transparent for white light by spoof surface plasmons,” Phys. Rev. Lett. 105(24), 243901 (2010).
[CrossRef]

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[CrossRef] [PubMed]

K. G. Lee and Q. H. Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95(10), 103902 (2005).
[CrossRef] [PubMed]

K. Kobayashi, H. Aikawa, S. Katsumoto, and Y. Iye, “Tuning of the Fano effect through a quantum dot in an Aharonov-Bohm interferometer,” Phys. Rev. Lett. 88(25), 256806 (2002).
[CrossRef] [PubMed]

M. V. Rybin, A. B. Khanikaev, M. Inoue, K. B. Samusev, M. J. Steel, G. Yushin, and M. F. Limonov, “Fano resonance between Mie and Bragg scattering in photonic crystals,” Phys. Rev. Lett. 103(2), 023901 (2009).
[CrossRef] [PubMed]

Other (2)

Here, for simplicity, the potential contribution from the neighbor charges has been neglected. The counting of neighbor contribution will add more circuit parameters and modify (enlarge) the chain-mode dispersion. Nonetheless, no further physical understanding can be provided.

C. Kittel, Introduction to Solid State Physics (Wiley, 2005).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic view of the proposed plasmonic structure. (b) The unit cell [marked by dotted lines in (a)] with the corresponding structural parameters (the configuration of incident light is also shown). And (c) The FIB image of a part of the structure.

Fig. 2
Fig. 2

Simulated (a) and measured (b) zero-order transmission spectra for s-polarization. The solid and dotted lines correspond to the modified and pure slit array, respectively. The inset shows the calculated spectra of a single slit with (the solid line) and without (the dotted line) the periodic bumps as well as a Fano fit based on the Eq. (4). Here, the structural parameters are set as p = 600 nm, s = 300 nm, w = 150 nm, and l = 80 nm.

Fig. 3
Fig. 3

Simulated electric-field (a) and current-density (b) patterns for the transmission maximum [on x-y plane (z = −50 nm)]. The results for the minimum are just similar. (c) Schematic view of the linear chain employed in the theoretical model. Here, am and bm represent the quantities of the surface charges, and the thinner red arrows show the surface current flow (the light electric field is denoted by the thicker blue arrow).

Fig. 4
Fig. 4

Simulated transmission, reflection, and absorption spectra of the structure. The chain plasmon mode resonance corresponds to a strong absorption of the light.

Fig. 5
Fig. 5

Simulated (a) and measured (b) transmission spectra for various incident angles (the Fanolike resonance corresponds, from the left to right, to the incident angle 0, 10, 15, and 20 degrees, respectively). The inset presents the dispersion curve obtained using the spectral positions of simulated absorption maxima.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

L a m + R a m + a m + b m C 1 + a m + b m 1 C 2 = E m l , L b m + R b m + a m + b m C 1 + a m + 1 + b m C 2 = E m l .
p 0 = ( 2 l 2 / L ) [ ( 1 cos q d ) ω 2 2 ω 2 ] [ ω + 2 ( q ) ω 2 i η ω ] [ ω 2 ( q ) ω 2 i η ω ] E 0 .
ω ± 2 ( q ) = ω 1 2 + ω 2 2 ± ω 1 4 + ω 2 4 + 2 ω 1 2 ω 2 2 cos q d .
T = | t 0 α ω 2 ω 0 2 ω 2 i η ω | 2       =   t 0 2 | ( ω 2 ω 0 2 ) / ω + η ( α ω / t 0 η + i ) | 2 ( ω 2 ω 0 2 ) 2 / ω 2 + η 2       ~ t 0 2 | ω ω 0 + q F η / 2 | 2 ( ω ω 0 ) 2 + ( η / 2 ) 2 .

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